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For his science fair project, Bryan is comparing slime recipes. For one batch, he weighs out 9349\frac{3}{4} ounces of liquid starch and mixes it with 22 bottles of glue. For the other batch, he weighs out 7347\frac{3}{4} ounces of liquid starch and mixes it with 2122\frac{1}{2} bottles of glue. Both batches end up weighing the same amount.\newlineWhich equation can you use to find ww, the weight of a bottle of glue in ounces?\newlineChoices:\newline(A) 9.75+2w=7.75+2.5w9.75 + 2w = 7.75 + 2.5w\newline(B) 9.75−2w=7.75−2.5w9.75 - 2w = 7.75 - 2.5w\newlineHow much does a bottle of glue weigh?\newlineSimplify any fractions.\newline___\_\_\_ ounces

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Q. For his science fair project, Bryan is comparing slime recipes. For one batch, he weighs out 9349\frac{3}{4} ounces of liquid starch and mixes it with 22 bottles of glue. For the other batch, he weighs out 7347\frac{3}{4} ounces of liquid starch and mixes it with 2122\frac{1}{2} bottles of glue. Both batches end up weighing the same amount.\newlineWhich equation can you use to find ww, the weight of a bottle of glue in ounces?\newlineChoices:\newline(A) 9.75+2w=7.75+2.5w9.75 + 2w = 7.75 + 2.5w\newline(B) 9.75−2w=7.75−2.5w9.75 - 2w = 7.75 - 2.5w\newlineHow much does a bottle of glue weigh?\newlineSimplify any fractions.\newline___\_\_\_ ounces
  1. Understand the problem: Understand the problem.\newlineBryan has two batches of slime that weigh the same. The first batch uses 9349\frac{3}{4} ounces of liquid starch and 22 bottles of glue. The second batch uses 7347\frac{3}{4} ounces of liquid starch and 2122\frac{1}{2} bottles of glue. We need to find the weight of one bottle of glue, denoted as ww.
  2. Convert to improper fractions: Convert mixed numbers to improper fractions to make calculations easier.\newline9349 \frac{3}{4} ounces is (9×4+3)/4=394(9 \times 4 + 3)/4 = \frac{39}{4} ounces.\newline7347 \frac{3}{4} ounces is (7×4+3)/4=314(7 \times 4 + 3)/4 = \frac{31}{4} ounces.
  3. Set up the equation: Set up the equation.\newlineSince both batches weigh the same, the weight of the liquid starch plus the weight of the glue bottles must be equal for both batches. Therefore, the equation is:\newline(394)+2w=(314)+(52)w(\frac{39}{4}) + 2w = (\frac{31}{4}) + (\frac{5}{2})w, where ww is the weight of one bottle of glue.
  4. Convert to decimals: Convert the equation to decimals to simplify. \newline394\frac{39}{4} ounces is 9.759.75 ounces.\newline314\frac{31}{4} ounces is 7.757.75 ounces.\newline52\frac{5}{2} is 2.52.5.\newlineSo the equation in decimals is:\newline9.75+2w=7.75+2.5w9.75 + 2w = 7.75 + 2.5w
  5. Identify correct equation: Identify the correct equation from the choices.\newlineThe correct equation that represents the situation is:\newline(A) 9.75+2w=7.75+2.5w9.75 + 2w = 7.75 + 2.5w
  6. Solve for w: Solve the equation for w.\newlineSubtract 7.757.75 from both sides:\newline9.75−7.75+2w=2.5w9.75 - 7.75 + 2w = 2.5w\newline2+2w=2.5w2 + 2w = 2.5w\newlineSubtract 2w2w from both sides:\newline2=0.5w2 = 0.5w\newlineDivide both sides by 0.50.5 to find ww:\newlinew=2/0.5w = 2 / 0.5\newlinew=4w = 4

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